Multiplicity Of Solutions Of A Nonlinear Parabolic Equation

The existence and multiplicity of solutions are important components of the theory of partial differential equation.The researches for existence and multiplicity of solutions under boundary conditions are important subjects of partial differential equation.We investigate the existence of multiple solutions of the nonlinear equation under Dirichlet boundary condition onΩ, Lu-Dtu+g(u)=f(x,t). We also discuss a relation between multiplicity of solutions and the nonlinear perturbation of the equation.In section 1, introduction is given.In section 2, we introduce some important definitions and theorems.In section 3, we use variational reduction method and contraction mapping theorem to transform the problem from an infinite dimensional'one to a finite dimensional one.In section 4, we reveal a relation between multiplicity of solutions and the nonlinear perturbation of the equation.In section 5, we give the conclusion.